{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T05:25:17Z","timestamp":1697693117386},"reference-count":28,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2009,9,16]],"date-time":"2009-09-16T00:00:00Z","timestamp":1253059200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2009,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A new technique is presented for proving that a consequence system enjoys Craig interpolation or Maehara interpolation based on the fact that these properties hold in another consequence system. This technique is based on the existence of a back and forth translation satisfying some properties between the consequence systems. Some examples of translations satisfying those properties are described. Namely a translation between the global\/local consequence systems induced by fragments of linear logic, a Kolmogorov\u2010Gentzen\u2010G\u00f6del style translation, and a new translation between the global consequence systems induced by full Lambek calculus and linear logic, mixing features of a Kiriyama\u2010Ono style translation with features of a Kolmogorov\u2010Gentzen\u2010G\u00f6del style translation. These translations establish a strong relationship between the logics involved and are used to obtain new results about whether Craig interpolation and Maehara interpolation hold in that logics (\u00a9 2009 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200810013","type":"journal-article","created":{"date-parts":[[2009,9,16]],"date-time":"2009-09-16T18:24:37Z","timestamp":1253125477000},"page":"515-534","source":"Crossref","is-referenced-by-count":3,"title":["Interpolation via translations"],"prefix":"10.1002","volume":"55","author":[{"given":"Jo\u00e3o","family":"Rasga","sequence":"first","affiliation":[]},{"given":"Walter","family":"Carnielli","sequence":"additional","affiliation":[]},{"given":"Cristina","family":"Sernadas","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2009,9,16]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7091-9461-4_6"},{"key":"e_1_2_1_3_2","unstructured":"W.Carnielli J.Rasga andC.Sernadas Appendix on Interpolation via translations: proofs as expected. Technical report SQIG\u2010IT DM IST 2008. The appendix contains the full details of most of the proofs that are just sketched or not proved at all in the paper since they follow in an expected way. Available athttp:\/\/wslc.math.ist.utl.pt\/ftp\/pub\/RasgaJ\/08\u2010CRS\u2010it\u2010appendix.pdf."},{"key":"e_1_2_1_4_2","unstructured":"W. A.Carnielli M. E.Coniglio D.Gabbay P.Gouveia andC.Sernadas Analysis and Synthesis of Logics \u2013 How To Cut And Paste Reasoning Systems. Applied Logic 35 (Springer 2008)."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/exm061"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1021845424153"},{"key":"e_1_2_1_7_2","unstructured":"J.Czelakowski andD.Piggozi Amalgamation and interpolation in abstract algebraic logic. In: Models Algebras and Proofs (X. Caicedo and C. H. Montenegro eds.) Lecture Notes on Pure and Applied Mathematics 203 pp. 187\u2013265 (Dekker 1999)."},{"key":"e_1_2_1_8_2","doi-asserted-by":"crossref","unstructured":"D.Gabbay andL.Maksimova Interpolation and Definability: Modal and Intuitionistic Logics (Oxford University Press 2005).","DOI":"10.1093\/acprof:oso\/9780198511748.001.0001"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-006-8305-5"},{"key":"e_1_2_1_10_2","doi-asserted-by":"crossref","unstructured":"G.Gentzen On the relation between intuitionist and classical arithmetic. In: The Collected Papers of Gerhard Gentzen (M. Szabo ed.) pp. 53\u201367 (North Holland 1969). English translation of [10].","DOI":"10.1016\/S0049-237X(08)70821-8"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02015371"},{"key":"e_1_2_1_12_2","first-page":"183","article-title":"Sur quelques points de la logique de M. Brouwer","volume":"15","author":"Glivenko V.","year":"1929","journal-title":"Academie Royale de Belgique, Bulletins de la Classe des Sciences"},{"key":"e_1_2_1_13_2","unstructured":"K.G\u00f6del Zur intuitionistischen Arithmetik und Zahlentheorie. In: Ergebnisse eines mathematischen Kolloquiums volume 4 pp. 34\u201338 (1933). English translation: [13]."},{"key":"e_1_2_1_14_2","unstructured":"K.G\u00f6del On intuitionistic arithmetic and number theory. In: Collected Works Vol I pp. 287\u2013295 (Oxford University Press 1986). English translation of [12]."},{"key":"e_1_2_1_15_2","unstructured":"E.Hoogland Definability and interpolation: Model\u2010theoretic investigations. (PhD Thesis Amsterdam 2001)."},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1521-3870(200001)46:1<135::AID-MALQ135>3.0.CO;2-R"},{"key":"e_1_2_1_17_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200610036"},{"key":"e_1_2_1_18_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00370189"},{"key":"e_1_2_1_19_2","first-page":"646","article-title":"On the principle \u201ctertium non datur\u201d","volume":"32","author":"Kolmogorov A. N.","year":"1924","journal-title":"Mathematicheski\u012d Sbornic"},{"key":"e_1_2_1_20_2","unstructured":"A. N.Kolmogorov On the principle of excluded middle. In: From Frege to G\u00f6del: a Source Book in Mathematical Logic 1879\u20101931 (J. van Heijenoort ed.) pp. 416\u2013437 (Harvard University Press 1967). English translation of [18]."},{"key":"e_1_2_1_21_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0027763000010023"},{"key":"e_1_2_1_22_2","unstructured":"S.Maehara On the interpolation theorem of Craig. S\u00fbgaku12(1960\u20101961)."},{"key":"e_1_2_1_23_2","unstructured":"M.Okada andK.Terui Completeness proofs for linear logic based on the proof search method (preliminary report). In: Proceedings of the Symposium on Type Theory and Its Applications (J. Garriguej ed.) pp. 146\u2013168 (University of Kyoto 1998)."},{"key":"e_1_2_1_24_2","doi-asserted-by":"crossref","unstructured":"H.Ono Proof\u2010theoretic methods in nonclassical logic \u2013 an introduction. In: Theories of types and proofs volume 2 of MSJ Mem. pp. 207\u2013254. (Math. Soc. Japan 1998).","DOI":"10.2969\/msjmemoirs\/00201C060"},{"key":"e_1_2_1_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2007.08.001"},{"key":"e_1_2_1_26_2","doi-asserted-by":"publisher","DOI":"10.2307\/2275398"},{"key":"e_1_2_1_27_2","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1190150298"},{"key":"e_1_2_1_28_2","unstructured":"J.Shoenfield Mathematical Logic. 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